An electronic assembly consists of two subsystems $A$ and $B$. Past testing procedures data show that probabilities of failure are $P(A \text{ fails}) = 0.2$, $P(B \text{ fails alone}) = 0.15$, and $P(A \cap B \text{ fail}) = 0.15$. Then the probability that $A$ fails alone is equal to

The sum of all the elements in the set $\{n \in \{1, 2, \ldots, 100\} \mid \text{H.C.F. of } n \text{ and } 2040 \text{ is } 1\}$ is equal to $.....$

If $n(U) = 600$,$n(A) = 100$,$n(B) = 200$,and $n(A \cap B) = 50$,then $n(\bar{A} \cap \bar{B})$ is: ($U$ is the universal set and $A$ and $B$ are subsets of $U$)

Of the members of three athletic teams in a school,$21$ are in the cricket team,$26$ are in the hockey team,and $29$ are in the football team. Among them,$14$ play hockey and cricket,$15$ play hockey and football,and $12$ play football and cricket. Eight play all the three games. The total number of members in the three athletic teams is:

Let $S = \{1, 2, 3, 5, 7, 10, 11\}$. The number of nonempty subsets of $S$ such that the sum of all elements is a multiple of $3$ is $........$

The sum of all integers from $1$ to $100$ that are divisible by $2$ or $5$ is...........